Question

How do you find the derivative of `f(x)=1/4x^2-x+4`?

Answer 1

`1/2x-1`

Explanation:

To find the derivative of a polynomial, we can use the sum/difference rules for differentiation, which means that we can take the derivative of each term separated by an addition/subtraction sign separately.

First, let's find the derivative of the first term by using the power rule, which states that the derivative of `x^n` is `nx^(n-1)`:

When there's a constant in front of a variable, just put the constant to the side for the moment and focus on differentiating the non-constant variable. After that is done, the constant should be multiplied by the new derivative that is obtained.

`1/4x^2` becomes `1/4(2*x^(2-1))`, which in turn becomes `1/2x`.

Next, let's take the derivative of the second term, which is `-x`, and the derivative of a variable by itself is just 1. Taking into account the negative sign, this turns out to be `-1`.

The last term is a constant, and the derivative of any constant is `0`, so that will replace the 4.

Combining all of our answers together, our final result is `1/2x-1`.